263 research outputs found
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
We study supersymmetric gauge theories with an R-symmetry, defined on
non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a
supersymmetry-preserving quotient of Euclidean AdS. We compute the exact
partition function in these theories, using the method of localization, thus
reducing the problem to the computation of one-loop determinants around a
supersymmetric locus. We evaluate the one-loop determinants employing three
different techniques: an index theorem, the method of pairing of eigenvalues,
and the heat kernel method. Along the way, we discuss aspects of supersymmetry
in manifolds with a conformal boundary, including supersymmetric actions and
boundary conditions.Comment: v3:79p, minor clarifications and references adde
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating
divergences in observables in asymptotically locally AdS spacetimes. For dual
boundary field theories which are supersymmetric it is natural to ask whether
this defines a supersymmetric renormalization scheme. Recent results in
localization have brought this question into sharp focus: rigid supersymmetry
on a curved boundary requires specific geometric structures, and general
arguments imply that BPS observables, such as the partition function, are
invariant under certain deformations of these structures. One can then ask if
the dual holographic observables are similarly invariant. We study this
question in minimal N = 2 gauged supergravity in four and five dimensions. In
four dimensions we show that holographic renormalization precisely reproduces
the expected field theory results. In five dimensions we find that no choice of
standard holographic counterterms is compatible with supersymmetry, which leads
us to introduce novel finite boundary terms. For a class of solutions
satisfying certain topological assumptions we provide some independent tests of
these new boundary terms, in particular showing that they reproduce the
expected VEVs of conserved charges.Comment: 70 pages; corrected typo
Effect of Phosphorus and Strontium Additions on Formation Temperature and Nucleation Density of Primary Silicon in Al-19 Wt Pct Si Alloy and Their Effect on Eutectic Temperature
The influence of P and Sr additions on the formation temperature and nucleation density of primary silicon in Al-19 wt pct Si alloy has been determined, for small volumes of melt solidified at cooling rates _T of ~0.3 and 1 K/s. The proportion of ingot featuring primary silicon decreased
progressively with increased Sr addition, which also markedly reduced the temperature for first formation of primary silicon and the number of primary silicon particles per unit volume �Nv: When combined with previously published results, the effects of amount of P addition and cooling rate on �Nv are in reasonable accord with �Nv� _T ¼ ðp=6fÞ1=2 109 [250 � 215 (wt pct P)0.17]�3, where �Nv is in mm�3, _T is in K/s, and f is volume fraction of primary silicon.
Increased P addition reduces the eutectic temperature, while increased Sr appears to generate a minimum in eutectic temperature at about 100 ppmw Sr
Twisted characters and holomorphic symmetries
We consider holomorphic twists of arbitrary supersymmetric theories in four
dimensions. Working in the BV formalism, we rederive classical results
characterizing the holomorphic twist of chiral and vector supermultiplets,
computing the twist explicitly as a family over the space of nilpotent
supercharges in minimal supersymmetry. The BV formalism allows one to work with
or without auxiliary fields, according to preference; for chiral superfields,
we show that the result of the twist is an identical BV theory, the holomorphic
system with superpotential, independent of whether or not
auxiliary fields are included. We compute the character of local operators in
this holomorphic theory, demonstrating agreement of the free local operators
with the usual index of free fields. The local operators with superpotential
are computed via a spectral sequence, and are shown to agree with functions on
a formal mapping space into the derived critical locus of the superpotential.
We consider the holomorphic theory on various geometries, including Hopf
manifolds and products of arbitrary pairs of Riemann surfaces, and offer some
general remarks on dimensional reductions of holomorphic theories along the
-sphere to topological quantum mechanics. We also study an
infinite-dimensional enhancement of the flavor symmetry in this example, to a
recently-studied central extension of the derived holomorphic functions with
values in the original Lie algebra that generalizes the familiar Kac--Moody
enhancement in two-dimensional chiral theories
Constraints on chiral operators in N=2 SCFTs
Open Access, © The Authors. Article funded by SCOAP3.
This article is distributed under the terms of the Creative Commons
Attribution License (
CC-BY 4.0
), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited
Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
We consider the conformal field theory of N complex massless scalars in 2+1
dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a
't Hooft large N limit, keeping fixed \lambda = N/k. We compute some
correlation functions in this theory exactly as a function of \lambda, in the
large N (planar) limit. We show that the results match with the general
predictions of Maldacena and Zhiboedov for the correlators of theories that
have high-spin symmetries in the large N limit. It has been suggested in the
past that this theory is dual (in the large N limit) to the Legendre transform
of the theory of fermions coupled to a Chern-Simons gauge field, and our
results allow us to find the precise mapping between the two theories. We find
that in the large N limit the theory of N scalars coupled to a U(N)_k
Chern-Simons theory is equivalent to the Legendre transform of the theory of k
fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization
of the latter theory. We conjecture that perhaps this duality is valid also for
finite values of N and k, where on the fermionic side we should now have (for
N_f flavors) a U(k)_{N-N_f/2} theory. Similar results hold for real scalars
(fermions) coupled to the O(N)_k Chern-Simons theory.Comment: 49 pages, 16 figures. v2: added reference
Supercurrent anomalies in 4d SCFTs
We use holographic renormalization of minimal \mathcalN=2 gauged
supergravity in order to derive the general form of the quantum Ward identities
for 3d \mathcalN=2 and 4d \mathcalN=1 superconformal theories on
general curved backgrounds, including an arbitrary fermionic source for the
supercurrent. The Ward identities for 4d \mathcalN=1 theories contain both
bosonic and fermionic global anomalies, which we determine explicitly up to
quadratic order in the supercurrent source. The Ward identities we derive apply
to any superconformal theory, independently of whether it admits a holographic
dual, except for the specific values of the and anomaly coefficients,
which are equal due to our starting point of a two-derivative bulk supergravity
theory. In the case of 4d \mathcalN=1 superconformal theories, we show that
the fermionic anomalies lead to an anomalous transformation of the supercurrent
under rigid supersymmetry on backgrounds admitting Killing spinors, even if all
anomalies are numerically zero on such backgrounds. The anomalous
transformation of the supercurrent under rigid supersymmetry leads to an
obstruction to the -exactness of the stress tensor in supersymmetric vacua,
and may have implications for the applicability of localization techniques. We
use this obstruction to the -exactness of the stress tensor in order to
resolve a number of apparent paradoxes relating to the supersymmetric Casimir
energy, the BPS condition for supsersymmetric vacua, and the compatibility of
holographic renormalization with supersymmetry, that were presented in the
literature
Seiberg duality for Chern-Simons quivers and D-brane mutations
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best
understood as the low energy theory of D2-branes on a dual type IIA background.
We show how the D2-brane point of view naturally leads to three dimensional
Seiberg dualities for Chern-Simons quivers with chiral matter content: They
arise from a change of brane basis (or mutation), in complete analogy with the
better known Seiberg dualities for D3-brane quivers. This perspective
reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills
theories with unitary gauge groups. We provide explicit examples of dual
theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment
on the string theory derivation of CS quivers dual to massive type IIA
geometries.Comment: 32 pages+appendix; v2: added a referenc
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